A finiteness result for associated primes of local cohomology modules

Brodmann, M.; Faghani, A.

doi:10.1090/S0002-9939-00-05328-4

A finiteness result for associated primes of local cohomology modules
HTML articles powered by AMS MathViewer

by M. P. Brodmann and A. Lashgari Faghani PDF

Proc. Amer. Math. Soc. 128 (2000), 2851-2853 Request permission

Abstract:

We show that the first non-finitely generated local cohomology module $H^i_\mathfrak {a} (M)$ of a finitely generated module $M$ over a noetherian ring $R$ with respect to an ideal $\mathfrak {a}\subseteq R$ has only finitely many associated primes.

References

Brodmann, M., Rotthaus, Ch., Sharp, R., On annihilators and associated primes of local cohomology modules, to appear in Journal of Pure and Applied Algebra
Brodmann, M, Sharp, R., Local cohomology – an algebraic introduction with geometric applications, Cambridge studies in advanced mathematics No. 60, Cambridge University Press, 1998
Gerd Faltings, Der Endlichkeitssatz in der lokalen Kohomologie, Math. Ann. 255 (1981), no. 1, 45–56 (German). MR 611272, DOI 10.1007/BF01450555
Mordechai Katzman, Finiteness of $\bigcup _e\textrm {Ass}\,F^e(M)$ and its connections to tight closure, Illinois J. Math. 40 (1996), no. 2, 330–337. MR 1398098
Leif Melkersson and Peter Schenzel, Asymptotic prime ideals related to derived functors, Proc. Amer. Math. Soc. 117 (1993), no. 4, 935–938. MR 1124148, DOI 10.1090/S0002-9939-1993-1124148-8
K. N. Raghavan, Local-global principle for annihilation of local cohomology, Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992) Contemp. Math., vol. 159, Amer. Math. Soc., Providence, RI, 1994, pp. 329–331. MR 1266189, DOI 10.1090/conm/159/01513